{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Factorial Mixture",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "DgBkBx32yaMY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "##### Copyright 2018 The TensorFlow Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "metadata": {
        "id": "gWHuBAw5BCaa",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "yvRjEiD3exsq",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Factorial Mixture\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Factorial_Mixture.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Factorial_Mixture.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "metadata": {
        "id": "c9ZrVm6_xTLp",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "In this notebook we show how to use [TensorFlow Probability](https://github.com/tensorflow/probability) (TFP) to sample from a factorial Mixture of Gaussians distribution defined as:\n",
        "$$p(x_1, ..., x_n) = \\prod_i p_i(x_i)$$ where: $$\\begin{align*} p_i &\\equiv \\frac{1}{K}\\sum_{i=1}^K \\pi_{ik}\\,\\text{Normal}\\left(\\text{loc}=\\mu_{ik},\\, \\text{scale}=\\sigma_{ik}\\right)\\\\1&=\\sum_{k=1}^K\\pi_{ik}, \\forall i.\\hphantom{MMMMMMMMMMM}\\end{align*}$$\n",
        "\n",
        "Each variable $x_i$ is modeled as a mixture of Gaussians, and the joint distribution over all $n$ variables is a product of these densities.\n",
        "\n",
        "Given a dataset $x^{(1)}, ..., x^{(T)}$, we  model each dataponit $x^{(j)}$ as a factorial mixture of Gaussians:\n",
        "$$p(x^{(j)}) = \\prod_i p_i (x_i^{(j)})$$\n",
        "\n",
        "\n",
        "Factorial mixtures are a simple way of creating distributions with a small number of parameters and a large number of modes."
      ]
    },
    {
      "metadata": {
        "id": "DGFnQOpxw5FS",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "import tensorflow_probability as tfp\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "tfd = tfp.distributions\n",
        "\n",
        "# Use try/except so we can easily re-execute the whole notebook.\n",
        "try:\n",
        "  tf.enable_eager_execution()\n",
        "except:\n",
        "  pass"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "pr6_6GpGdW-E",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Build the Factorial Mixture of Gaussians using TFP"
      ]
    },
    {
      "metadata": {
        "id": "ioCED18abzwn",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "num_vars = 2        # Number of variables (`n` in formula).\n",
        "var_dim = 1         # Dimensionality of each variable `x[i]`.\n",
        "num_components = 3  # Number of components for each mixture (`K` in formula).\n",
        "sigma = 5e-2        # Fixed standard deviation of each component.\n",
        "\n",
        "# Set seed. Remove this line to generate different mixtures!\n",
        "tf.set_random_seed(77)\n",
        "\n",
        "# Choose some random (component) modes.\n",
        "component_mean = tfd.Uniform().sample([num_vars, num_components, var_dim])\n",
        "\n",
        "factorial_mog = tfd.Independent(\n",
        "   tfd.MixtureSameFamily(\n",
        "       # Assume uniform weight on each component.\n",
        "       mixture_distribution=tfd.Categorical(\n",
        "           logits=tf.zeros([num_vars, num_components])),\n",
        "       components_distribution=tfd.MultivariateNormalDiag(\n",
        "           loc=component_mean, scale_diag=[sigma])),\n",
        "   reinterpreted_batch_ndims=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "U_E2Zf--eJ0C",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Notice our use of `tfd.Independent`. This \"meta-distribution\" applies a `reduce_sum` in the `log_prob` calculation over the rightmost `reinterpreted_batch_ndims` batch dimensions. In our case, this sums out the variables dimension leaving only the batch dimension when we compute `log_prob`.  Note that this does not affect sampling."
      ]
    },
    {
      "metadata": {
        "id": "-uAYBsTNdveL",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Plot the Density\n",
        "Compute the density on a grid of points, and show the locations of the modes with red stars. Each mode in the factorial mixture corresponds to a pair of modes from the underlying individual-variable mixture of Gaussians. We can see 9 modes in the plot below, but we only needed 6 parameters (3 to specify the locations of the modes in $x_1$, and 3 to specify the locations of the modes in $x_2$). In contrast, a mixture of Gaussians distribution in the 2d space $(x_1, x_2)$ would require 2 * 9 = 18 parameters to specify the 9 modes."
      ]
    },
    {
      "metadata": {
        "id": "ym9qrhAxXdch",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "outputId": "5791a3b2-5301-4e07-bd05-cd85f6733346"
      },
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(6,5))\n",
        "\n",
        "# Compute density.\n",
        "nx = 250 # Number of bins per dimension.\n",
        "x = np.linspace(-3 * sigma, 1 + 3 * sigma, nx).astype('float32')\n",
        "vals = tf.reshape(tf.stack(np.meshgrid(x, x), axis=2), (-1, num_vars, var_dim))\n",
        "probs = factorial_mog.prob(vals).numpy().reshape(nx, nx)\n",
        "\n",
        "# Display as image.\n",
        "from matplotlib.colors import ListedColormap\n",
        "cmap = ListedColormap(sns.color_palette(\"Blues\", 256))\n",
        "p = plt.pcolor(x, x, probs, cmap=cmap)\n",
        "ax = plt.axis('tight');\n",
        "\n",
        "# Plot locations of means.\n",
        "means_np = component_mean.numpy().squeeze()\n",
        "for mu_x in means_np[0]:\n",
        "  for mu_y in means_np[1]:\n",
        "    plt.scatter(mu_x, mu_y, s=150, marker='*', c='r', edgecolor='none');\n",
        "plt.axis(ax);\n",
        "\n",
        "plt.xlabel('$x_1$')\n",
        "plt.ylabel('$x_2$')\n",
        "plt.title('Density of factorial mixture of Gaussians');"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAFNCAYAAADmc9PrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEIiIiIiYYfz/zhgXWEMthcEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f64dd116b00>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "DhktSkSzdxpr",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Plot samples and marginal density estimates"
      ]
    },
    {
      "metadata": {
        "id": "7B33PnrWc09U",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "outputId": "722db1a0-ef64-476f-f995-f96f5058585c"
      },
      "cell_type": "code",
      "source": [
        "samples = factorial_mog.sample(1000).numpy()\n",
        "\n",
        "g = sns.jointplot(\n",
        "    x=samples[:, 0, 0],\n",
        "    y=samples[:, 1, 0],\n",
        "    kind=\"scatter\",\n",
        "    stat_func=None,\n",
        "    marginal_kws=dict(bins=50))\n",
        "g.set_axis_labels(\"$x_1$\", \"$x_2$\");"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbQAAAG0CAYAAABaNNJGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f64c65082b0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}